Independent of parameter

Show that the evaluation of the pullback of a constant 1-form [tex] k_{1}dx + k_{2}dy + k_{3}dz [/tex] over the directed line segment from [tex] \bold{r} [/tex] to [tex] \bold{s} [/tex] does not depend on which linear parameterization is chosen.

Show that the evaluation of the pullback of a constant 1-form [tex] k_{1}dx + k_{2}dy + k_{3}dz [/tex] over the directed line segment from [tex] \bold{r} [/tex] to [tex] \bold{s} [/tex] does not depend on which linear parameterization is chosen.

So [tex] (x,y,z) = \bold{r} + t(\bold{s}-\bold{r}) [/tex]. Then what?

Τhen, you observe that the coefficients of the 1-form are constant, and will remain so
no matter what (x,y,z) you choose.

Ps. Yeap, I am answering old questions.
Got time on my hands and need to kill it... Is that so bad? :grumpy: